Extinction of some strains and asymptotic profiles of coexistence endemic equilibria in a multi-strain epidemic model

Abstract

This work studies the asymptotic dynamics of classical solutions of a multi-strain diffusive epidemic model in spatially heterogeneous environments. Results on the nonexistence of coexistence endemic equilibria are established. Moreover, explicit conditions on the parameters range which guarantee the extinctions of some strains of the disease are examined. In particular, we establish that the competition-exclusion principle occurs when the population diffuses very fast and one strain uniquely maximizes the ratio of the spatial average of transmission rate over that of the recovery rate. However, several strains of the disease may coexist when either: (i) the population diffuses very slowly, (ii) or a subgroup diffuses very slowly and the other subgroup diffuses very fast. In these two scenarios, the asymptotic profiles of the coexistence endemic equilibria with respect to the diffusion rates of the population are presented. In particular, we observe a spatial segregation of the infected populations when they diffuse very slowly.